In conversational question answering (CQA), the task of question rewriting~(QR) in context aims to rewrite a context-dependent question into an equivalent self-contained question that gives the same answer. In this paper, we are interested in the robustness of a QR system to questions varying in rewriting hardness or difficulty. Since there is a lack of questions classified based on their rewriting hardness, we first propose a heuristic method to automatically classify questions into subsets of varying hardness, by measuring the discrepancy between a question and its rewrite. To find out what makes questions hard or easy for rewriting, we then conduct a human evaluation to annotate the rewriting hardness of questions. Finally, to enhance the robustness of QR systems to questions of varying hardness, we propose a novel learning framework for QR that first trains a QR model independently on each subset of questions of a certain level of hardness, then combines these QR models as one joint model for inference. Experimental results on two datasets show that our framework improves the overall performance compared to the baselines.